Abstract
This paper presents a new lattice-gas method for molecular dynamics modeling. A mean-field treatment is given and is applied to a linear stability analysis. Exact numerical simulations of the solid-phase crystallization are presented, as is a finite-temperature multiphase liquid-gas system. The lattice-gas method, a discrete dynamical method, is therefore capable of representing a variety of collective phenomena in multiple regimes from the hydrodynamic scale down to a molecular dynamics scale.
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References
C. Appert, D. d'Humières, V. Pot, and S. Zaleski, Three-dimensional lattice gas with minimal interactions,Transport Theory Stat. Phys. 23(1–3):107–122 (Proceedings of Euromech 287—Discrete Models in Fluid Dynamics, P. Nelson, ed.).
C. Appert and S. Zaleski, Lattice gas with a liquid-gas transition,Phys. Rev. Lett. 64:1–4 (1990).
P. L. Bhatnagar, E. P. Gross, and M. Krook, A model for collision processes in gases. i. Small amplitude processes in charged and neutral one-component systems,Phys. Rev. 94(3):511–525 (1954).
Hudong Chen, Shiyi Chen, and W. H. Mattaeus, Recovery of the Navier-Stokes equations using a lattice-gas Boltzmann method,Phys. Rev. A 45(8):R5339-R5342 (1992).
Shiyi Chen, Hudong Chen, D. Martínez, and W. Matthaeus, Lattice Boltzmann model for simulation of magnetohydrodynamics,Phys. Rev. Lett. 67(27):3776–3779 (1991).
U. Frisch, D. d'Humières, B. Hasslacher, P. Lallemand, Y. Pomeau, and J.-P. Rivet, Lattice gas hydrodynamics in two and three dimensions,Complex Systems 1:649–707 (1987).
M. Hénon, Viscosity of a lattice gas, inLattice Gas Methods for Partial Differential Equations, G. D. Doolean, ed. (Addison-Wesley, Reading, Massachusetts, 1990).
L. P. Kadanoff and J. Swift, Transport coefficients near the critical point: A master-equation approach,Phys. Rev. 165(1):310–322 (1967).
L. D. Landau and E. M. Lifshitz,Fluid Mechanics, 2nd ed. (Pergamon Press, Oxford, 1987).
Y. H. Qian, D. d'Humières, and P. Lallemand, Lattice BGK models for Navier-Stokes equation,Europhys. Lett. 17(6bis):479–484 (1992).
D. H. Rothman, From ordered bubbles to random stripes—Pattern-formation in a hydrodynamic lattice-gas,J. Stat. Phys. 71(3–4):641–652 (1993).
Xiaowen Shan and Hudong Chen, Simulation of nonideal gases and liquid-gas phase transitions by the lattice Boltzmann equation,Phys. Rev. E 49(4):2941–2948 (1994).
S. Wolfram, Cellular automaton fluids I: Basic theory,J. Stat. Phys. 45(3/4):471–526 (1986).
J. Yepez, Lattice-gas dynamics on the cm-5 and cam-8, inSecond Annual Technical Interchange Symposium Proceedings (Phillips Laboratory, PL/XPP, 1993), Vol. I, p. 217.
J. Yepez, A reversible lattice-gas with long-range interactions coupled to a heat bath, inProceedings of the Pattern Formation and Lattice-Gas Automata NATO Advanced Research Workshop, R. Kapral and A. Lawniczak, eds. (American Mathematical Society, Providence, Rhode Island, 1993).
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Yepez, J. Lattice-gas crystallization. J Stat Phys 81, 255–294 (1995). https://doi.org/10.1007/BF02179979
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DOI: https://doi.org/10.1007/BF02179979